



'''simple docstring'''

import random






def 				a  (     UpperCamelCase_    :    int			)       ->	bool:
		snake_case__	     =num - 1
		snake_case__	     =0

		while s % 2 == 0:
				snake_case__	     =s // 2
				t += 1

		for _ in range(5			):
				snake_case__	     =random.randrange(2      ,					num - 1			)
				snake_case__	     =pow(UpperCamelCase_      ,					UpperCamelCase_      ,					UpperCamelCase_			)
				if v != 1:
						snake_case__	     =0
						while v != (num - 1):
								if i == t - 1:
										return False
								else:
										snake_case__	     =i + 1
										snake_case__	     =(v**2) % num
		return True






def 				a  (     UpperCamelCase_    :    int			)       ->	bool:
		if num < 2:
				return False

		snake_case__	     =[
		    2,
		    3,
		    5,
		    7,
		    11,
		    13,
		    17,
		    19,
		    23,
		    29,
		    31,
		    37,
		    41,
		    43,
		    47,
		    53,
		    59,
		    61,
		    67,
		    71,
		    73,
		    79,
		    83,
		    89,
		    97,
		    101,
		    103,
		    107,
		    109,
		    113,
		    127,
		    131,
		    137,
		    139,
		    149,
		    151,
		    157,
		    163,
		    167,
		    173,
		    179,
		    181,
		    191,
		    193,
		    197,
		    199,
		    211,
		    223,
		    227,
		    229,
		    233,
		    239,
		    241,
		    251,
		    257,
		    263,
		    269,
		    271,
		    277,
		    281,
		    283,
		    293,
		    307,
		    311,
		    313,
		    317,
		    331,
		    337,
		    347,
		    349,
		    353,
		    359,
		    367,
		    373,
		    379,
		    383,
		    389,
		    397,
		    401,
		    409,
		    419,
		    421,
		    431,
		    433,
		    439,
		    443,
		    449,
		    457,
		    461,
		    463,
		    467,
		    479,
		    487,
		    491,
		    499,
		    503,
		    509,
		    521,
		    523,
		    541,
		    547,
		    557,
		    563,
		    569,
		    571,
		    577,
		    587,
		    593,
		    599,
		    601,
		    607,
		    613,
		    617,
		    619,
		    631,
		    641,
		    643,
		    647,
		    653,
		    659,
		    661,
		    673,
		    677,
		    683,
		    691,
		    701,
		    709,
		    719,
		    727,
		    733,
		    739,
		    743,
		    751,
		    757,
		    761,
		    769,
		    773,
		    787,
		    797,
		    809,
		    811,
		    821,
		    823,
		    827,
		    829,
		    839,
		    853,
		    857,
		    859,
		    863,
		    877,
		    881,
		    883,
		    887,
		    907,
		    911,
		    919,
		    929,
		    937,
		    941,
		    947,
		    953,
		    967,
		    971,
		    977,
		    983,
		    991,
		    997,
		]

		if num in low_primes:
				return True

		for prime in low_primes:
				if (num % prime) == 0:
						return False

		return rabin_miller(UpperCamelCase_			)






def 				a  (     UpperCamelCase_    :    int = 1024			)       ->	int:
		while True:
				snake_case__	     =random.randrange(2 ** (keysize - 1)      ,					2 ** (keysize)			)
				if is_prime_low_num(UpperCamelCase_			):
						return num


if __name__ == "__main__":
			SCREAMING_SNAKE_CASE__     :						Tuple	=  generate_large_prime()
			print(('''Prime number:''', num))
			print(('''is_prime_low_num:''', is_prime_low_num(num)))









'''simple docstring'''

import os

SCREAMING_SNAKE_CASE__     :						Optional[Any]	=  {'''I''': 1, '''V''': 5, '''X''': 1_0, '''L''': 5_0, '''C''': 1_0_0, '''D''': 5_0_0, '''M''': 1_0_0_0}






def 				a  (     UpperCamelCase_    :    str			)       ->	int:
		snake_case__	     =0

		snake_case__	     =0
		while index < len(UpperCamelCase_			) - 1:
				snake_case__	     =SYMBOLS[numerals[index]]
				snake_case__	     =SYMBOLS[numerals[index + 1]]
				if current_value < next_value:
						total_value -= current_value
				else:
						total_value += current_value
				index += 1
		total_value += SYMBOLS[numerals[index]]

		return total_value






def 				a  (     UpperCamelCase_    :    int			)       ->	str:
		snake_case__	     =''

		snake_case__	     =num // 1000
		numerals += m_count * "M"
		num %= 1000

		snake_case__	     =num // 100
		if c_count == 9:
				numerals += "CM"
				c_count -= 9
		elif c_count == 4:
				numerals += "CD"
				c_count -= 4
		if c_count >= 5:
				numerals += "D"
				c_count -= 5
		numerals += c_count * "C"
		num %= 100

		snake_case__	     =num // 10
		if x_count == 9:
				numerals += "XC"
				x_count -= 9
		elif x_count == 4:
				numerals += "XL"
				x_count -= 4
		if x_count >= 5:
				numerals += "L"
				x_count -= 5
		numerals += x_count * "X"
		num %= 10

		if num == 9:
				numerals += "IX"
				num -= 9
		elif num == 4:
				numerals += "IV"
				num -= 4
		if num >= 5:
				numerals += "V"
				num -= 5
		numerals += num * "I"

		return numerals






def 				a  (     UpperCamelCase_    :    str = "/p089_roman.txt"			)       ->	int:
		snake_case__	     =0

		with open(os.path.dirname(UpperCamelCase_			) + roman_numerals_filename			) as filea:
				snake_case__	     =filea.readlines()

		for line in lines:
				snake_case__	     =line.strip()
				snake_case__	     =parse_roman_numerals(UpperCamelCase_			)
				snake_case__	     =generate_roman_numerals(UpperCamelCase_			)
				savings += len(UpperCamelCase_			) - len(UpperCamelCase_			)

		return savings


if __name__ == "__main__":
			print(f"""{solution() = }""")




